All categories

3 years ago

1.The two legs of a right triangle measures 3 feet and 2 feet. What is the length of the hypotenuse?

Mathematics

1 answer:

Dominik [7]3 years ago

4 0

Answer:

5; you add the two legs for the hypotenuse

Step-by-step explanation:

You might be interested in

can someone show me how to find the general solution of the differential equations? really need to know how to do it for the upc

mariarad [96]

The first equation is linear:

$x\dfrac{\mathrm dy}{\mathrm dx}-y=x^2\sin x$

Divide through by $x^2$ to get

$\dfrac1x\dfrac{\mathrm dy}{\mathrm dx}-\dfrac1{x^2}y=\sin x$

and notice that the left hand side can be consolidated as a derivative of a product. After doing so, you can integrate both sides and solve for $y$ .

$\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1xy\right]=\sin x$
$\implies\dfrac1xy=\displaystyle\int\sin x\,\mathrm dx=-\cos x+C$
$\implies y=-x\cos x+Cx$

- - -

The second equation is also linear:

$x^2y'+x(x+2)y=e^x$

Multiply both sides by $e^x$ to get

$x^2e^xy'+x(x+2)e^xy=e^{2x}$

and recall that $(x^2e^x)'=2xe^x+x^2e^x=x(x+2)e^x$ , so we can write

$(x^2e^xy)'=e^{2x}$
$\implies x^2e^xy=\displaystyle\int e^{2x}\,\mathrm dx=\frac12e^{2x}+C$
$\implies y=\dfrac{e^x}{2x^2}+\dfrac C{x^2e^x}$

- - -

Yet another linear ODE:

$\cos x\dfrac{\mathrm dy}{\mathrm dx}+\sin x\,y=1$

Divide through by $\cos^2x$ , giving

$\dfrac1{\cos x}\dfrac{\mathrm dy}{\mathrm dx}+\dfrac{\sin x}{\cos^2x}y=\dfrac1{\cos^2x}$
$\sec x\dfrac{\mathrm dy}{\mathrm dx}+\sec x\tan x\,y=\sec^2x$
$\dfrac{\mathrm d}{\mathrm dx}[\sec x\,y]=\sec^2x$
$\implies\sec x\,y=\displaystyle\int\sec^2x\,\mathrm dx=\tan x+C$
$\implies y=\cos x\tan x+C\cos x$
$y=\sin x+C\cos x$

- - -

In case the steps where we multiply or divide through by a certain factor weren't clear enough, those steps follow from the procedure for finding an integrating factor. We start with the linear equation

$a(x)y'(x)+b(x)y(x)=c(x)$

then rewrite it as

$y'(x)=\dfrac{b(x)}{a(x)}y(x)=\dfrac{c(x)}{a(x)}\iff y'(x)+P(x)y(x)=Q(x)$

The integrating factor is a function $\mu(x)$ such that

$\mu(x)y'(x)+\mu(x)P(x)y(x)=(\mu(x)y(x))'$

which requires that

$\mu(x)P(x)=\mu'(x)$

This is a separable ODE, so solving for $\mu$ we have

$\mu(x)P(x)=\dfrac{\mathrm d\mu(x)}{\mathrm dx}\iff\dfrac{\mathrm d\mu(x)}{\mu(x)}=P(x)\,\mathrm dx$
$\implies\ln|\mu(x)|=\displaystyle\int P(x)\,\mathrm dx$
$\implies\mu(x)=\exp\left(\displaystyle\int P(x)\,\mathrm dx\right)$

and so on.

6 0

4 years ago

A game that has a take of two cards with 10 red guards for two girls and two yellow cards are you randomly choose to go to find

Svetach [21]

Answer:

The probability of choosing two red cards would be 3/8

Step-by-step explanation:

The probability of choosing 1 red card is 10/16; the probability of choosing a second red card would then be 9/15.

P(2 red) = 10/16(9/15) = 90/240 = 3/8.

3 0

3 years ago

-3x > 24 on a number line

lianna [129]

$\text {Hey! Here is the number line you requested}$

$\text {This equation will also equal...}$

$x$

$\text {How do you get that answer?}$ $\text {Simple! You just divide both sides by 3}$

$-3x/3>24/-3$

$\text {Final Answer}$

$x$

$\text {Best of Luck!}$

$\text {-LimitedX}$

4 0

3 years ago

HELP ASAP! I need the answer to all 3 of these questions.

Leokris [45]

Answer:

I think that number one is 26, two is -4, and three is -4

Step-by-step explanation:

To solve for number one replace 8 with (x) so 3(8) + 2. 3 x 8 = 24 and 24+2 = 26

Numbers 2 and 3 appear to be the same problem so just do 3(-2) + 2 (Because you replace the number with the x) 3(-2) = -6 + 2 = -4!

I hope that helped!

3 0

3 years ago

Each side of a square is increasing at a rate of 2 cm/s. at what rate is the area of the square increasing when the area of the

faltersainse [42]

Let x(t) = the length of a side of the square (cm) at time t (s).
The rate of change of x is given as
$\frac{dx}{dt} =2 \, \frac{cm}{s}$

The area (cm²) at time t is
A = x²

The rate of change of the area with respect to time is
$\frac{dA}{dt} = \frac{dA}{dx} \frac{dx}{dt} =2 \frac{dA}{dx} =2(2x)=4x \, \frac{cm^{2}}{s}$

When A = 9 cm², then x = √9 = 3cm. Hence obtain
$\frac{dA}{dt} = 4(3) = 12 \, \frac{cm^{2}}{s}$

Answer: 12 cm²/s

3 0

3 years ago